Temporal-Place Limen

What it is

The Temporal-Place Limen (colloquially: the Auditory Horizon) is the perceptual phase transition at approximately 25.8Hz — a period length of 38.7ms — at which periodic signals cross the boundary between two distinct modes of human auditory perception: rhythm and pitch.

Below ~25.8Hz, the ear tracks individual events. The repeating pattern is perceived as rhythm — discrete pulses with felt intervals between them. Above ~25.8Hz, the ear fuses repetitions into a continuous sensation. The pattern is perceived as pitch — a sustained frequency with a recognisable tonal character.

This boundary is not a hard cliff. Psychoacoustic research identifies a transition zone between approximately 10Hz and 40Hz, characterised by two intermediate perceptual states:

• Flutter (~10–20Hz): events too fast to track individually but not yet fused into a stable pitch; a rapid flickering sensation
• Roughness (~20–40Hz): fusion beginning, pitch emerging but unstable, perceived as a coarse or buzzing tone

The Temporal-Place Limen is provisionally defined at ~25.8Hz (triangulated via Local Closure) as the midpoint of this transition zone — the point at which perceptual mode is most evenly balanced between rhythm and pitch, and therefore the most structurally meaningful single value to use as an anchor.

Physiological basis: Temporal vs place coding

Temporal coding is how the auditory nerve represents lower frequencies: individual neurons fire in sync with specific phases of the sound wave itself (phase-locking), so the timing pattern of the spikes directly mirrors the timing pattern of the acoustic signal — this is why, in this range, rhythm and pitch can both be read straight off the firing pattern without any further inference. Place coding takes over as frequency rises past what neurons can physically track cycle-by-cycle (the phase-locking ceiling, roughly in the low kHz range but with the effective breakdown for rhythmic/periodic perception happening much lower): instead of timing, the cochlea encodes frequency by where along the basilar membrane the vibration peaks, exploiting its natural tonotopic structure (base = high frequencies, apex = low). Past that ceiling, individual event-timing is no longer available in the neural signal at all — the system has switched from “when did it happen” to “where did it peak,” which is a different kind of code carrying different information. This is why “temporal-place limen” is the more honest name for the boundary: it’s not a property of periodicity in the mathematical sense, it’s the specific point where the ear’s encoding strategy itself changes from one physiological mechanism to another.

Why this is the correct anchor

Standard measures of musical time — Hz for frequency, BPM for tempo — are derived from the second, which is itself a fraction of Earth’s rotation period: an astronomical unit that became a time unit by historical convention. It has no relationship to human perception, acoustic physics, or musical structure. The second is to musical time measurement what Fahrenheit is to temperature: a unit whose reference points are determined by historical contingency rather than the phenomenon being measured.

The Temporal-Place Limen is determined instead by human auditory neurology — specifically the temporal resolution limits of the basilar membrane and auditory nerve firing rates. It is:

• Not a convention — it is a property of the biological instrument that receives music
• Not culturally contingent — it is stable across humans regardless of musical tradition or training
• Not astronomically derived — it is grounded in the perceptual system that music is addressed to
• Intrinsic to PPT’s theoretical structure — the framework already treats the pitch/rhythm boundary as theoretically significant; the Temporal-Place Limen is the precise location of that boundary

This makes it the correct choice for an anchor in the same sense that absolute zero is the correct anchor for temperature measurement in physics: it is the structurally meaningful zero point of the phenomenon being described, not a convenient approximation of it.

Relationship to conventional measures

The Temporal-Place Limen can be expressed in conventional units — 25.8Hz, 38.7ms period, ~1548 BPM — but these are interface translations, not primary descriptions. The theoretical status of ~25.8Hz as an anchor does not depend on seconds; the second is available as a translation layer when interfacing with conventional tools, instruments, and notation systems.

The relationship is analogous to Kelvin and Celsius: Celsius remains useful for everyday temperature description, but Kelvin is the theoretically correct system because its zero point is grounded in molecular physics rather than water’s behaviour. BPM and Hz remain useful for performance and notation, but the Temporal-Place Limen coordinate system is theoretically correct because its anchor is grounded in auditory perception rather than Earth’s rotation.

The upper boundary

A second physiological boundary exists at approximately 20kHz — the upper limit of human pitch perception, also determined by basilar membrane resolution. This is designated the Upper Temporal-Place Limen (colloquially: the Upper Auditory Horizon).

The full audible pitch range spans from the Temporal-Place Limen (~25.8Hz) to the Upper Temporal-Place Limen (20kHz). This range is:

log2(20000 / 25.8) = log2(775.19) ≈ 9.6 octaves

Approximately 9.6 octaves — spanning Metric DuPeriods −9.6 to 0 in PPT’s unified coordinate system. See Metric DuPeriod for the full coordinate definition.

Dual register

The term Temporal-Place Limen is used in formal, academic, and psychoacoustic contexts, consistent with established psychoacoustic vocabulary (limen: Latin for threshold; cf. absolute limen, difference limen).

The colloquial name Auditory Horizon is used in pedagogical, explanatory, and cross-reference contexts. The horizon metaphor captures the character of the boundary: it is not that periodicity ceases to exist on either side, but that the nature of perception changes — just as a horizon changes what can be seen, not what exists.

This dual-register convention follows the pattern established elsewhere in PPT: formal specification paired with an accessible working name.

See also

• Amplitude and Time — the physical grounding; the second as astronomical convention
• Periodicity — the perceptual rate boundary as a property of human perception, not underlying structure
• Metric DuPeriod — the coordinate system anchored to the Temporal-Place Limen
• Metric DuPeriod — Extended Range — the stratospheric positive metric DuPeriod space above musical form